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Recent progress on the boundary rigidity problem


Authors: Plamen Stefanov and Gunther Uhlmann
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 64-70
MSC (2000): Primary 53C20
DOI: https://doi.org/10.1090/S1079-6762-05-00148-4
Published electronically: June 23, 2005
MathSciNet review: 2150946
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Abstract | References | Similar Articles | Additional Information

Abstract: The boundary rigidity problem consists in determining a compact, Riemannian manifold with boundary, up to isometry, by knowing the boundary distance function between boundary points. In this paper we announce the result of our forthcoming article that one can solve this problem for generic simple metrics. Moreover we probe stability estimates for this problem.


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Additional Information

Plamen Stefanov
Affiliation: Department of Mathematics, Purdue University, West Lafayette, IN 47907
Email: stefanov@math.purdue.edu

Gunther Uhlmann
Affiliation: Department of Mathematics, University of Washington, Seattle, WA 98195
Email: gunther@math.washington.edu

DOI: https://doi.org/10.1090/S1079-6762-05-00148-4
Keywords: Boundary rigidity, Riemannian manifold, inverse problem
Received by editor(s): March 8, 2005
Published electronically: June 23, 2005
Additional Notes: The first author was supported in part by NSF Grant DMS-0400869.
The second author was supported in part by NSF Grant DMS-0245414.
Communicated by: Dmitri Burago
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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